Okay, after analyzing your code I see that this happens because the structure is not the same as the example it proposes. You generate this:
<label class="...">
<input type="radio" class="..." value="..." checked="checked">PayPal
</label>

Styling radio button is a little tricky thing, actually we will hide the default radio button under one layer, where the new layer will deal with our custom style. You can test using the following code

Sai, is it possible without editing the HTML or PHP? If you look at this file: https://github.com/restrictcontentpro/restrict-content-pro/blob/master/templates/register-single.php
you can see there are already some classes: rcp_gateways_fieldset, rcp_gateway_fields
Can we use this instead, or not?